Subgroups — C₅⋊(C₁₁⋊(D₇₃⋊C₃)) #37562813

Order 24090.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₀₁₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊(D₇₃⋊C₃)	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₇₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₅⋊(D₇₃⋊C₃)	—	11	1	no	maximal, Hall
7	D₈₀₃	—	5	1	no	Hall
8	C₅×C₇₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₃₆₅	—	11	1	no	Hall
11	D₇₃⋊C₃	—	55	1	no	Hall
12	C₅×C₇₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅₅	—	73	1	no	maximal, Hall
14	C₇₃⋊C₃	D₅₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	—	73	1	no	Hall
16	D₇₃	—	55	1	no	Hall
17	D₅₅	—	73	1	no	Hall
18	C₇₃	C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	—	365	1	no	Hall
20	C₅×C₁₁	D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	—	73	1	no	Hall
22	C₃×D₅	—	803	1	no	Hall
23	D₁₁	—	365	1	no	Hall
24	C₃×C₅	—	73	1	no	Hall
25	C₁₁	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	803	1	no	Hall
27	C₂×C₃	—	4015	1	no	Hall
28	C₅	C₁₁⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	73	1	no	Sylow
30	C₂	—	4015	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₁₁×C₇₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.